Rare Hadronic B Decays

1

Rare Hadronic B Decays

John Fry

Lepton Photon 2003

John Fry Lepton Photon 2003 2

Scope of Talk

• To present updated branching fractions (BF) and CP asymmetries (ACP) for rare (charmless) B decay modes

• To show how BF and ACP are used with theoretical models to put constraints on the Standard Model and to search for New Physics.

NB: All results are preliminary unless referenced.


How Good is the Standard Model?

A. Hööcker et al, Eur. Phys. Jour.

C21 (2001) 225, [hep-ph/0104062]

K [K] and B sectors [md,Vub , Vtd , Sin (2)]consistent with each other and SM (theory)

LEP Coupling Constants

CPLEAR• T consistent with CP• Tight CPT constraint


Motivation for Rare Decays

• SM is a very good approximation to reality

Hence

• Need to consider processes where is small in order to be sensitive to new physics.

• Hence processes dominated by penguin loops, or CKM - suppressed decays

NPSMCommon AA

SMA


Procedure

• Compare nature (precise, experimental measurements) with SM (theoretical models) for sensitive quantities.

• Agreement gives an alternative route to (, ) and additional constraints on the unitarity triangle.

• Disagreement means:– New Physics …. OR

– Refinements needed to theoretical calculations … ….AND Model-independent calculations needed


The (theoretical) Problem

BM1

M2

How to go from here …

to branching fractions and CP asymmetry


Classes of theoretical calculations

• QCD Factorisation (mb >> QCD)

Amps factorise to LO ( / mb), all orders S

Naïve factorisation recovered in LO

• PhenomenologyAmplitudes of dominant processes related to

measured BF and each other via SU(3)

• Model “Independent”Isospin & minimal dynamical assumptions

bounds on deviations from SM

Beneke, Buchalla, Neubert & SachrajdaNucl Phys B606 (2001) 245Beneka & Neubert Hep-ph / 0308039

Chiang, Rosner Phys Rev D65 074035Chiang et al Hep-ph / 0307395Lipkin Phys Lett B254 (1991) 247

Grossman, Ligeti, Nir, QuinnHep-ph / 0303171


Visualising QCD Factorisation

+B

m

M

B

M

m

<MmQB> = FBm T * fM M + FBM T * fm m + T fB B * fM M * fm m

TTF

BM

m


Pictorial Phenomenology

+B

m

M

B

M

m

TTF

+

Leading Order – Naive Factorisation


Direct CP ViolationCP asymmetry occurs if the decay B f ( and its charge conjugate) is mediated by two amplitudes with different strong and weak phases:

)cos()cos(2

)sin()sin(2

12122122

21

12122122

22

)(2

)(1

)(2

)(1

2211

2211

aaaa

aa

aa

aaA

eaeaa

eaeaa

ff

ff

CP

iif

iif : strong phase CP-even

: weak phase CP-odd

Naïve Expectation:ACP small for K (0+) Dominant penguin (tree)ACP large for -+ Unless dynamically suppressed


Overview of B Production and Decay

z

ee

S4

K

0recB

Inclusive Reconstruction B-Flavor Tagging

Exclusive B Meson Reconstruction

CP eigenstates

Flavor eigenstates

PEP-2 (SLAC)

0tagB

Flavor eigenstates Resolution function and Tagging

Signal: Branching fraction; ACP; CP Analysisflavrec BB

Signalrec BB


Signal Selection

2*2beamES

*BpEm *

beam* EEE B

(mES) 2.6 MeV/c2 (E) 20 MeV


Discrimination of B and Continuum

Combine into a Fisher (or NN)

Signalu,d,s,cbackground

Fisher Discriminant

Arb

itra

ry U

nit

sMonte Carlo

B produced (almost) at rest in Y(4S) frame

Isotropic B Jetty Continuum


Search for B0 → p pbar @ BaBar

p

K e

Use the DIRC to reject K, , e,

C.L.) %90( 107.2)(r 70 ppBSmallest upper-limit BF in B0/Bdecays!

C.L.) %90( 5.7

syst)(stat)(3.0 0.12.1

1.30.2

SN

Signal Eff = 91%Background Eff = 3%

Total signal efficiency = 37%




Summary of BF (10-6) for K, and KKMode BaBar Belle CLEO Average

K+ - 17.9 0.9 0.7

18.5 1.0 0.7 18.0 2.3 1.2 18.1 0.8

K0 + 17.5 1.8 1.3

22.0 1.9 1.1 18.8 3.7 2.1 19.6 1.5

K+ 0 12.8 1.2 1.0

12.8 1.4 1.2 12.9 2.4 1.2 12.8 1.1

K0 0 10.4 1.5 0.8

12.6 2.4 1.4 12.8 4.0 1.7 11.2 1.4

+ - 4.7 0.6 0.2 4.4 0.6 0.3 4.5 1.4 0.5 4.6 0.4

+ 0 5.5 1.0 0.6 5.3 1.3 0.5 4.6 1.8 0.7 5.3 0.8

0 0 2.1 0.6 0.3 1.7 0.6 0.3 < 4.4 1.90 0.47

K+ K- < 0.6 < 0.7 < 0.8 < 0.6

K+ K0 < 1.3 < 3.4 < 3.3 < 1.3

K0 K0 < 1.6 < 3.2 < 3.3 < 3.2


HFAGJ Smith (Colorado)J Alexander (Cornell)


Belle

Belle

Belle152 106 BB140 fb-1

Signal 3.4 25.6

BF (10-6)1.7 ± 0.6 ± 0.2

+9.3 -8.4


BaBar 0 0

Sub to PRL

BaBar124 106 BB113 fb-1

Signal 4.2 46 ± 13 ± 3

BF (10-6)2.1 ± 0.6 ± 0.3


BBNS NPB606 (2001) 245

Inconsistent ?

Data (2001)

Data (2003)

QCD_F: Ratios of & K BF’s

0.42 ± 0.11


Comparison of BF and ACP with Theory‡

Mode BFExp

(10-6)

BF pQCD

(10-6)

ACP Expt

(%)

ACP pQCD

(%)

ACP QCDF

(%)

K+- 18.2 ± 0.8 13 – 19 -9 ± 3† -13 – -22 +5 ± 10

K0+ 19.6 ± 1.5 14 – 26 -1 ± 6 -0.6 – -1.5 0 ± 1

K+0 12.8 ± 1.1 8 – 14 0 ± 7 -10 – -17 +7 ± 10

K00 11.2 ± 1.4 8 – 14 3 ± 37 -3 ± 4

+- 4.55 ± 0.44 6 – 11 16 – 30 -6 ± 13

+0 5.3 ± 0.8 2.7 – 4.8 -7 ± 14 0 -2 ± 5

00 1.90 ± 0.47 0.33 – 0.65 45 ± 60

† Belle: -8.8 ± 3.5 ± 1.8 BaBar -10.7 ± 4.1 ± 1.2

‡ Keum and Sanda hep-ph/0306004Beneke and Neubert hep-ph/0308039


Belle


Disentangling the Bh+h- contributions (I)

B h+h- from hadronic triggerIncludes Bd BsKK, BsK ,

and Bd K

Monte-Carlo plot below shows:Bd Bs K+K- Bs K± ±,

& Bd K± ± (From Monte-Carlo)all pile up in the same region

Must disentangle contributions from each mode To do this we use:-Kinematical variable separation M vs =(1-p1/p2)q1

-dE/dx based K and identification

CDF


Disentangling the Bh+h- contributions (II)

M vs a for each Bh+h- mode dE/dx calibration using D*± D0, D0 K±± ( from D* unambiguously distinguishes K, from D0)

Sanity check: Measure Ratio of Branching RatiosCDF : (Bd -)/(Bd K+-) = 0.26 ±0.11±0.055, PDG: 0.13 0.010.29

0.12 0.02

Yield for each mode:Bd Bd K± ±Bs K± ±Bs K+K- (stat) (stat)First observation !

Method works ! Confirmed by Sanity check against ratio of branching ratiosHave first observation of Bs K+K-Its a CP Eigenstate: Can use thisTo measure s as well !!

CDF


Disentangling the Bh+h- contributions

(Blessed CDF results)

• ACP(BdK = 0.02 ± 0.15(stat) ± 0.017(syst)

• BR(Bd/BR(BdK=

0.26 ± 0.11(stat) ± 0.055(syst)

• fs X BR(BsKK)/fd X BR(BdK) =

0.74 ± 0.20(stat) ± 0.22(syst)

•Yield of BsKK = 90 ±17(stat) ±17(syst) events


Is Rescattering Important?

• Could modify branching fractions and CP asymmetries in and K decays, complicating extraction of and

• KK decays are more sensitive to rescattering– Could have significant enhancement through (for example) DD

or intermediate states

0K

K0 u

u

su

sd

u

d

BaBar P_QCD*

K+K- <0.6 0.05

K+K0 <2.2 1.7

K0K0 <1.6 1.8

BF(10-6)

No sign of rescattering (FSI) yet

*Chen and Li, Phys. Rev D63, 014003 (2000)


BF & ACP for B , K, , KMode BF (10-6)

(BaBar)BF (10-6) (Belle)

ACP % (BaBar)

ACP % (Belle)

B0 → ρ+ π- 22.6 2.8 29.1 6.4 -11 7 -38 21

B0 → ρ+ K- 7.3 1.8 15.1 4.1 19 18 22 23

B0 → ρ0 π0 < 2.5 6.0 3.1

B+ → ρ+ π0 11.0 2.7 23 17

B+ → ρ0 π+ 9.3 1.3 8.0 2.3 -17 11

B+ → ρ0 K+ < 6.2 < 12

B0 → ω K0 5.3 1.4 < 7.6

B+ → ω K+ 5.0 1.1 6.7 1.4 -5 16 6 20

B0 → ω π0 < 3

B+ → ω π+ 5.4 1.1 5.9 1.5 4 17 48 23


Belle B , K

K+

+

KS


BaBar: B K Dalitz Plot

B+ K*0(892)+, K*0K+ -

10.3±1.2+1.0

B+ f0(980)K+, f0 + 9.2±1.2+2.1

B+ c0 K+, c0 + 1.46±0.35±0.12

B+ D0+, D0 K+ - 184.6±3.2±9.7

B+higher K*0+, K*0K+-

25.1±2.0+11.0

B+ 0(770)K+, 0 + < 6.2

B+ K+ - + (non resonant) < 17

B+ higher fK+, f + <12

-5.7

-2.6

-2.7

K*0(892)K*0(higher)D0

ρ0

f0(980)

c0

56.4 fb-1

Branching Fractions 10 -6


Belle: Dalitz Plot Amplitude Analysis140 fb-1 B+ K+K+K- (Signal 1400) and K++ - (Signal 2584)

Resonances: K++ - K*(890), K*(1430), (770), c0(3400), f0(980), X(1350)K+K+K- (1020), C0(3400), X(1500)

Background parameterisation – fitted with large (7*) sideband sample

)()( * BWKBWeAk

skBG

ij

Signal parameterisation – fix masses, widths except X, f0

sNon

ppR

iRSignal e

s

ae

s

aeaA R

Re23

2

12

1 21

Fit to signal + background and determine amplitudes and phases



Belle DP Mass and Helicity Projections K


Belle Branching Fractions from Dalitz Plot




Longitudinal Polarisation B → V V

fL = L /

100% Pol CP evenExpect: fL ~ 1 – O(M2

V/M2B)

B0 + -

NS = 93 ±22±9BaBar [> 5]

Cos(1) MES


BelleB + 0


B → ρ ρ and ρ K* [BaBar & Belle]

(Errors approximated)

BF (10-6) ACP % Long. Poln %

B0→ ρ0 ρ0 < 2.1 (90 % CL)

B0→ ρ+ ρ- 27 ± 7 ± 6 99 ± 7 ± 3

B+→ ρ+ ρ0

Belle

22.5 ± 5.7 ± 5.8

31.7 ± 7.1 ± 6.7

-19 ± 23 ± 3

0 ± 22 ± 3

97 ± 7 ± 4

95 ± 11 ± 2

B+→ ρ0 K*+ 10.6 ± 3.0 ± 2.4 20 ± 32 ± 4 96 ± 15 ± 4

• CP asymmetries consistent with zero

• Polarisation in agreement with expectation


Why we need Theorists

K0++0

3* ~ udubVV2* ~ cscbVV

Mode CKM (fdecay)2 Ratio Exp Ratio BF (10-6)

K0+ 1 1 1 1 19.6

K*0+ 1 1.85 1.85 0.65 12.7

+0 2 0.66 0.03 0.27 5.3

+0 2 1.71 0.085 0.46 9.1

+0 2 2.9 0.145 1.35 26.4

The VPSTE effect (Form factor corrections at 40% level)


The unique decays B 0 0 and 0 0

Grossman Quinn boundPRD 58 (1998) 017504

BF give model-independentlimits to the CP angle

)(

)(;

)(

)()(sin

0

000

0

0002

BBF

BBFor

BBF

BBFEff

)%90(55.045.055.4

45.09.1)(sin 2 CLEff

)%90(10.0827

1.2)(sin 2 CLEff

| - Eff| < 50o () and < 20o () at 90% CL

+ - is dominantly longitudinal polarised, CP-even final state


B K(*) BaBar & Belle

q

q

s

s

u u

B+,0

K(*)

Mode BF (10-6) ACP (%) Polarisation %

K0 7.6 ± 1.4 9.0 ± 2.2

K+ 10.0 ± 1.0 9.4 ± 1.3 4 ± 9 1 ± 13

K*0 11.2 ± 1.5 10.0 ± 1.8 4 ± 12 7 ± 16 65 ± 7 43 ± 10

K*+ 12.7 ± 2.4 6.7 ± 2.2 16 ± 17 -13 ± 31 46 ± 12

• Expect similar BF all modes

• BF(+) < 4 10-7 [90% CL]No indication for rescattering – as KK

•Polarisation unexpectedly small


Belle


BR(B±K±) at CDF

• BR(B±K±) /BR(B±J/K±) = 0.0068 ±0.0021 (stat.) ± 0.0007 (syst.)

Using PDG 2002 for BR(B±J/K±):

• BR(B±K±) = (6.9 ± 2.1 (stat.) ± 0.8 (syst.)) x 10-6


B (')K(*) and ('), BaBar and Belle

Mode BF (10-6)

Belle BaBar

K+ 5.3 ± 1.9 2.8 ± 0.8

K0 < 4.6

' K+ 78 ± 11 76.9 ± 5.6

' K0 68 ± 13 55.4 ± 6.6

+ 5.4 ± 2.1 4.2 ± 1.0

' + < 7 2.8 ± 1.33.4

0 < 5.5

Mode BF (10-6)

Belle BaBar

K*+ 26.5 ± 8.4 25.7 ± 4.2

K*0 16.5 ± 4.8 19.0 ± 2.6

' K*+ < 90 < 12

' K*0 < 20 < 6.4

+ < 6.2 10.5 ± 3.44.8

' + 14.0 ± 5.43.8

' 0 < 14


Theoretical background: (') K, K * modes

Similarly for K 0, K *0 except no external tree

K, K*enhanced

K, K*suppressed

Interference

Flavour singlet diagram:

Also important for K*

CKM suppressed

H Lipkin Phys Lett B254 (1991) 247



B (')K(*) and , BaBar and Belle

Mode ACP (%)

Belle BaBar

K+ -32 ± 22

K0

' K+ -2 ± 7 4 ± 5

' K0

+ -51 ± 20

Mode ACP (%)

Belle BaBar

K*+ 15 ± 14

K*0 3 ± 11

' K*+

' K*0

+ 6 ± 29

Large asymmetry predicted for + , small for +

Chiang, Gronau, Luo, Rosner and Suprun [hep-ph/0307395]






How does theory stack up?

• Good phenomenological understanding of Branching Fractions for 2-body PP and PV decays

[Chiang et al hep-ph/0307395; Beneke et al hep-ph/0308039; Keum et al hep-ph/0306004]

• Factorisation models give insight into dynamics, but:– BF for 0 0 looks to be in disagreement with all predictions– BF for K, ' K, K* final states underestimated in QCDF[Annihilation contribution may be too large Aleksan et al, hep-ph/0301165]

• Asymmetry data is not yet precise enough to test models

• There is still a considerable role for model-independent theoretical calculations


When is it safe to claim New Physics?

For B0 KS, 'KS, K+K-KS we expect to measure:

S = sin(2) + , C = , where = O (2)

If S and C are measured precisely (S, C << 2 = 0.05)

Claim new physics if: |C| > 5, or |S- sin(2)| > 5

might be enhanced: Grossman bounds using isospin

u, cb s

)( 2*

*

Oa

a

VV

VVc

u

cscb

usub

relations and ratios of BFs.(K+K-KS) 0.2, ('KS) 0.5

GLNQ Hep-ph / 0303171

Must measure 20 BFs preciselyto improver the limit on !u-amplitude might be large


Summary – What have we learned?

• Precision measurements of branching fractions are testing factorisation models – to destruction??

• Precise measts of ACP will enable further tests of models. Is there a hint of a signal in K+- ?

• B K, K*,'K, 'K* are now almost understood, but polarisation << 100% in K* is a puzzle

• Measuring the BF for 0 0 is a triumph, but the value is surprisingly high. Increased focus on 00 for | - eff|

• Measurement of many more decay modes is needed to make model-independent tests of NP meaningful

• The expected increase in luminosity of the B Factories promises a continuing, rich harvest of physics

Documents

Rare Hadronic B Decays